Cost nothing to the user, yes. You can then have the state, a sophisticated purchaser, decide what it's willing to pay.

Not at all. The majority of the cost is subsidised by the Government who acts as a central purchaser to minimise profiteering and keep prices down.

Everyone pays a little bit towards it all via general taxation but if you prefer a system where individuals have to front the vast majority of their own costs, much of which is just being extracted as profit, then you are welcome to that. I prefer the option that leans a lot more towards socialism than rapacious capitalism.